Teleparallel Killing Vectors of Spherically Symmetric Spacetimes

TL;DR

This paper investigates the Killing vectors in spherically symmetric spacetimes within teleparallel gravity, comparing results with General Relativity and highlighting differences and potential conditions for agreement.

Contribution

It evaluates teleparallel Killing vectors for spherically symmetric and Friedmann spacetimes, revealing differences from GR and exploring conditions for consistency.

Findings

Seven Killing vectors in static spherically symmetric spacetimes

Six Killing vectors in Friedmann models within teleparallel gravity

Discrepancies between teleparallel gravity and General Relativity results

Abstract

In this paper, Killing vectors of spherically spacetimes have been evaluated in the context of teleparallel theory of gravitation. Further, we investigate the Killing vectors of the Friedmann metrics. It is found that for static spherically spacetimes the number of Killing vectors turn out to be \emph{seven} while for the Friedmann models, we obtain \emph{six} teleparallel Killing vectors. The results are then compared with those of General Relativity. We conclude that both of these descriptions of gravity do not provide the consistent results in general. However, these results may coincide under certain conditions for a particular spacetime.